What is the purpose and effect of using knuckles when kneading bread dough?

I don't think that it is really necessary to use your knuckles. Rather, there are ways to knead dough well, and ways to knead dough badly. I have seen ineffective people pinching the dough, or turning it between their hands, or other strange motions, which in a cargo-cult way resemble actual kneading, but don't do anything useful.

My guess is that whoever writes such instructions has learned a correct way of kneading that involves the knuckles, and writes down the admonishment to remind people that they have to do it right for the recipe to work well. The reason for the choice of label may be because the author is unaware that there are effective kneading methods which don't use the knuckles, or because the author has taught new kneaders and has found out that "use your knuckles" is a good cue to get them to use the right kind of motion.

A third possibility is that the author is referring specifically to the punching down step of a double-rise bread process. In that case, the motion between the first and second rise is not the same as standard kneading, and maybe the author wanted to underscore the difference.

This may not be the primary reason but I have hot hands and my knuckles are noticeably cooler than my palms or even the insides of my fingers. It's less of an issue with dough than with pastry but I still find that kneading with my palms makes the dough sticky compared to using my knuckles.

The writer is telling you a method for kneading. They can't the skill level of the user.

This is from my knowledge not books:

• Fingers only give 8 points of impression, which is a small area.
• Fingernails can leave bacteria. Although some modern cooks wear gloves to protect food.
• Using fingertips can cause injury to fingers nerves.
• It is a more efficient to use knuckles.
• It is less likely to remove gloves stuck to the dough (wrapping fingers tightly into a fist helps to hold gloves on)

This way a camper in the woods as well as a chef with nice equipment can get the same results.

Maybe knuckles impart more force compared to just using extended fingers (or the palm of your hands) when kneading the dough ?

I assume the "use knuckles" step is when you punch the dough after the first rise; it is just easier.

It might be intended to make kneading easier on one's wrists, especially for persons with weak wrists or joint problems.

When you knead with your palms, they are bent close to 90 degrees backward, which puts additional stress on the joints and ligaments. When you knead with your fists (knuckles) your wrists are (or should be) straight, which allows you to apply more force without stressing the joint. This will be especially beneficial if you knead a lot of dough (or for long time).